Many of the commentators seem truly baffled by Posner's Public Intellectuals.
Based on his reputation and their knowledge of him, they apparently find it hard not take something he writes seriously -- but this text seems to strike them as practically too bizarre.
A number suggest it might even be a sort of prank -- though almost all also back down from this after suggesting it and offer instead various rationalizations.
Among the comments:

David Brooks defends Posner, certain that: "No rational actor writes a sloppy book accusing the entire universe of American intellectuals of sloppiness; it's an act of reputational suicide."

Carol Polsgrove admits: "About midway through this chapter, I began entertaining the notion that Public Intellectuals might be a satire. Taken straight on, the book does not hold up."

The Economist notes: "Being a serious intellectual is harder than it looks. That is Mr Posner's point. But need he have illustrated it with this book ?"

Alan Wolfe wonders: "(D)oes his own contribution to the genre support or contradict his assertions about the decline in quality of this way of dealing with ideas ? The answer that immediately springs to mind is that Posner confirms his own thesis. (...) If this book is representative of what public intellectuals do, I can well understand his reservations about them. Still, I am reluctant to conclude that Posner is so anxious to prove his point about the low quality of public-intellectual work that he wrote a book designed to confirm it."

And Kenan Malik feels simply: "Public Intellectuals is not so much an analysis of decline as an expression of it."

In addition, there were the amused, bemused, and satirical commentaries from the likes of Christopher Hitchens and Carlin Romano, finding it easier -- like many others -- to poke fun than consider the text with any rigour.
It is an odd approach to a book, but one that proved surprisingly popular.

A major part of Posner's book -- the entire second-half -- focusses on case-studies of PIs at work; because of the subjective nature of much of what is presented here (as well as of the commentators' reactions) it is much more difficult to comment on critical reaction to this section -- at least where there was any.
Part Two is a significant part of the book, slightly shorter than than the first -- though still covering 175 pages -- but still hard to ignore.
It shows (or aims to, at least) the "different ways in which public intellectuals can go wrong" (p. 8).
Posner also claims this second part "substantiates claims in Part One" (ibid.).
One would expect it to attract some attention from the reviewers, but again many of them make a muddle of it.
Many choose not to explain that the book has this two-part format, and don't suggest (or even simply guess) specifically what Posner is trying to do in the second part.
And in some of the reviews, as well as most of the articles about the book (such as William Grimes' piece in The New York Times), one would be hard-pressed to even guess that Posner even offered anything resembling the second part of the book.
Indeed, it is astonishing how many of the reviews don't provide any sort of clarity about how Posner presents his argument or makes his case: readers are unlikely to have any sense of the outlines of the book -- beyond the fact that PIs are vilified and tabulated in it -- from the majority of the reviews.
A few reviewers do address the second part and Posner's descriptions and attacks -- notably Gertrude Himmelfarb, herself the target in a longer section in the chapter on "The Jeremiah School".
Others offer only confounding information -- the names of a few of the PIs Posner discusses, or an example or two of PI-work Posner attacks.
Space limitations serve as something of an excuse for why there are few refutations or extensive commentaries on the second half of Public Intellectuals in many of the reviews.
Nevertheless, the reviewers did a poor job of even simply conveying to readers what could be found there (and what Posner was trying to do there).

Reviewers and commentators approached Posner's Public Intellectuals in a variety of ways.
Several of the responses to the book were lengthy, few were thorough.
Much of the commentary was focussed on the tables and lists, but despite concentrating their attention on these it is here that commentators were most careless, ignoring and distorting many of Posner's own statements and explanations.
Many reviews were strident (with some even bordering on outrage), others jocular.
Few were neutral or straightforward, or tried to convey what Posner's intentions were.
A number of reviews did broadly convey what Posner's book was about and what arguments and data Posner offered, but almost all missed, ignored, or distorted significant parts of the book.
Several reviews are fairly informative -- notably Gertrude Himmelfarb's (if only by dint of its great length, perhaps allowing for more exposition than in the other reviews) -- but none provide an ideal introduction to the text, or to what potential readers should expect from Public Intellectuals.
Many reviews were misleading, and several were completely inadequate.
The non-review commentaries, aimed at a broader public, such as the articles in The Guardian and The New York Times were even worse.

Public Intellectuals is perhaps a difficult book to review, and the coverage of it might thus not make for an ideal case-study of the current state of book reviewing.
Much of Public Intellectuals is not clearly presented and makes it vulnerable to criticism.
Among its obvious faults: Posner doesn't simply offer one definition of PIs and stick to it, he compiles a list of PIs that inevitably is very contentious, he apparently doesn't explain very clearly what he wants to show with the data he collected and analyzed (essentially none of the commentators seem to have got what Posner was trying to do, and some of the fault must be attributed to Posner and how he presented this material), and he focusses (in the second part of the book) on an odd selection of PIs that don't ideally complement his findings from the first half of the book.
Some of the broad faults of Public Intellectuals are conveyed in the reviews -- but too few respond specifically to what Posner wrote and tried to show.
Many of the reviewers considered the book a failure, but most of these did not try to see it in terms of what Posner was arguing.
Too many focussed on the list of PIs and the faults found there, without considering that the composition of that list wasn't quite as important as they insisted it was -- something Posner repeatedly states, but which remained essentially ignored.

Book reviewing -- a craft in decline ?
One can't jump to conclusions from a single case.
Certainly, it is impossible to say whether the craft is in decline: we doubt it was ever much better.
And at least the book received a great deal of coverage -- reviews galore !
But the review coverage of Public Intellectuals was wholly inadequate and often unacceptably bad.
The picture the public got of the book (focussed almost entirely on Table 5.3) was completely wrong.
A great deal was said and written about this book, and most of it was completely irrelevant, serving as nothing more than entertainment (and certainly not information).
Indeed, reviewer-work -- at least in this case -- looks much like the PI-work Posner decries: reflecting "only a superficial engagement with the facts; (...) little better than kibitzing".

We at the complete review offer to our users not only our own humble and limited reviews of books, but also links to all other reviews we can find, as well as any additional relevant information (see, for example, our review of Public Intellectuals).
The more information and the more points of view the better, we like to think.
A book like this -- or rather: the reactions to a book like this -- make us wonder why we bother.
The reactions to Public Intellectuals completely overshadowed the book itself.
Lost in the shuffle was most of what Posner wrote: the commentaries and reviews presented the book in a way that bore little resemblance to Posner's text.
For cocktail party talk and the like the pseudo-summaries and and vague outlines of Posner's arguments and hypotheses probably suffice.
Perhaps that is what the reviews are there for anyway: to provide small-talk fodder, not actual information.
But that is a shame.
Posner suggests trying to hold PIs accountable for their (mis)statements.
What of reviewers ?
This piece is a small contribution, pointing out only a few faults and weaknesses in how some reviewers and commentators have addressed Posner's book.
But there is little opprobrium associated with finding mention here, and readers are always willing to forgive and forget -- or are simply indifferent.
To most it doesn't seem to be a big deal.
One thing one can grant many of the reviews and commentaries: they are entertaining.
Often emotionally charged, often funny (largely at Posner's expense), they make decent reads and are an amusing way to while away a few minutes.
That seems to be all the readers want.
The fact that the book under discussion is misrepresented, or inadequately represented, isn't of much interest.
Most probably don't imagine they'd ever even consider reading it anyway.
So this public reaction -- in the reviews, in the articles -- is likely the way the book will be remembered and how it will have an impact.
What valid (or invalid) points, approaches, and arguments Posner makes in the book are largely glossed over, lost under the popularized version found in the newspapers and magazines.
That can't be a good thing.